Effects of junctional correlations in the totally asymmetric simple exclusion process on random regular networks

TL;DR

This study explores how junctional correlations affect particle flow in a network model, revealing deviations from simple theories due to junction-induced slow bonds, with implications for understanding active transport.

Contribution

It introduces a pair mean-field theory and detailed analysis to account for junction correlations in the TASEP on random regular networks, highlighting their impact.

Findings

Junction correlations narrow the phase coexistence density range.

Density profiles decay algebraically with exponent 1/2 outside maximal-current phase.

Junctions act as effective slow bonds influencing transport dynamics.

Abstract

We investigate the totally asymmetric simple exclusion process on closed and directed random regular networks, which is a simple model of active transport in the one-dimensional segments coupled by junctions. By a pair mean-field theory and detailed numerical analyses, it is found that the correlations at junctions induce two notable deviations from the simple mean-field theory which neglects these correlations: (1) the narrower range of particle density for phase coexistence and (2) the algebraic decay of density profile with exponent $1/2$ even outside the maximal-current phase. We show that these anomalies are attributable to the effective slow bonds formed by the network junctions.